입회상담자료집 2008.4.16 6:27 PM 페이지1
MAC52 2400DPI 175LPI T
What is
?
The “E” in E.nopi MATH symbolizes
Education service provider
E-business leader
Eye level with each individual student
E.nopi MATH
Increases self-confidence
Strengthens concentration
Improves study habits
Develops critical thinking & analytical skills
Helps to develop mathematical thinking
Provides a self-feedback learning system
입회상담자료집 2008.4.16 6:27 PM 페이지2
MAC52 2400DPI 175LPI T
E.nopi MATH helps improve
problem-solving skills in school math.
Concept Cultivate problem-solving capabilities by improving
mathematical thinking
Development of
Mathematical Thinking
Basic
Thinking
Math
Critical
Thinking
Math
Structure
Basic Thinking Math
•Numbers
•Arithmetic
•Measurement
•Equations
Critical Thinking Math
Levels 1-23
Each level has 18 booklets.
Each level has 12 booklets.
Basic Thinking Math
•Numbers and Arithmetic
•Variables and Equations
•Relationships and Functions
•Probability and Statistics
•Geometry
•Measurement
Each level has 16 booklets.
•Patterns and Relationships
•Geometry
•Problem Solving
•Measurement
•Reasoning
Critical Thinking Math
Levels 24-32
•Problem SolvingⅠ
•Problem SolvingⅡ
•Problem SolvingⅢ
•Spatial Sense
Each level has 8 booklets.
3
입회상담자료집 2008.4.16 6:27 PM 페이지3
MAC52 2400DPI 175LPI T
Field of Study for E.nopi MATH
What is E.nopi’s Basic Thinking Math?
Levels 1-23
Basic Thinking Math
17
Level
Date
6
Name
Write the mixed number 2``‹!` as an improper fraction. (30 points)
Basic Thinking Math
23
Level
11
Find the surface area of a triangular prism. Fill in each
. (10 points each)
2``‹!`~=~ b ~+~`‹!`
=~:;‹:;~+~`‹!`
=~:;‹:;
It’s the sum of
the whole number
part and the
fraction part !
A Base area (1 Base)
6~\~
You can find the
area of a triangular
prism in the same way
as the trapezoidal
prism.
cm¤``
/~2~=
B Width of the lateral
Writing a Mixed Number as an Improper Fraction
[3\2]
~ +~6~+
cm
=
[denominator]\[whole number]
C Lateral area
cm¤``
\~7~=
[denominator]\[whole number]+[numerator]
D Surface area
\~2~+
Base area
9
Numbers (Number and Operations)
Students will learn natural numbers using the concepts
of number order and decimal notation. After learning
about fractions and decimals, students will be able to
work with rational numbers.
cm¤``
=
Lateral area
Yes! It’s easier to
find the surface
area of any prism by
opening it up.
When we open the
prism up, we can see
both lateral area and
base area at once.
10
Arithmetic (Number and Operations)
Students will learn and master the four operations
of arithmetic: addition, subtraction, multiplication,
and division.
Students will also learn to perform the four arithmetic
operations with fractions and decimals.
Basic Thinking Math
20
Level
10
Multiply. Simplify to the lowest terms. (8 points each)
A
2``‹@`~`\~z``°&`~`=
B
2``›!`~`\~z``·%`~`=
Basic Thinking Math
22
Level
8
Fill in each
C
2``·@`~`\~3``°#`~`=
D
3``ﬁ#`~`\~2``·@`~`=
E
2``‡@`~`\~2`⁄¡‚`~`=
F
4``ﬁ@`~`\~z`⁄¢⁄`~`=
A
. (8 points each)
1``›#`~\~x~=~3``¤!`!
{`1``›#`~`\~x``}~/
=~3``¤!`~`/~1``›#
x~=`~`¤&`~`\
x~=
B
x~/`~`‡$`~`=~2``°%
{`x~/~`‡$~}~\~`‡$`~`=~2``°%`~`\
x~=~
11
21
~\
8
x~=
Measurement
Equations with fractions can be solved easily by converting
mixed numbers into improper fractions.
5
Students will learn various units of measurement and
conversions of units of time, length, weight, and volume.
Students will also find the area and circumference of
2-dimensional figures. This knowledge will be further
extend to finding the surface area and volume of
3-dimensional figures.
4
Equations (Algebra)
Students will learn about equations, including the
concept of equality and solve for unknowns in
problems.
입회상담자료집 2008.4.16 6:27 PM 페이지4
MAC52 2400DPI 175LPI T
Levels 24-32
Basic Thinking Math
24
Level
16
1
3
Calculate {- 1 }÷{- 1 }÷{-5} using two different methods.
2
2
Basic Thinking Math
25
Level
13
Calculate one by one from the left.
Solve the following equations, then check your answers.
{-;2!;}÷{-;2#;} ÷(-5) = {-;2!;}_{
Basic Thinking Math
31
}÷(-5)
Level
A
={
}÷(-5)
={
}_{-;5!;}
-1.2x-0.9 = -0.7x+0.6
Solution
8
Name
Check
-1.2x-0.9 = -0.7x+0.6
-12x-9 = -7x+6
-12x+7x = 6+9
=
Date
(Left side): -1.2_
(Right side): -0.7_
The graph of y = a(x-p)2+q with a vertex at the
coordinates (-2, -2) is shown on the right. By
looking at the graph, find the values of a, p, and q.
-0.9 = 2.7
+0.6 = 2.7
y
1
-2
-5x =
x
O
-2
x=
We need to calculate by switching the
divisor with its reciprocal and converting
division to multiplication.
B
0.17-0.09x = -0.07-0.15x
Check
Calculate all terms at once.
{-;2!;}÷{-;2#;} ÷(-5)
= -{;2!; ÷;;;;;;;;;;;;÷
Find the equation of a quadratic function that has its line of symmetry at
x =-3 and passes through points (2, 6) and (-4, 3). Fill in the
boxes.
First, determine the sign.
}
1
= -{;2!; _;;;;;;;;;;;;_;;;;;;;;;;;;}
Convert division to
multiplication.
= -;;;;;;;;;;;;
Calculate the product of
three numbers at once.
C
0.19-0.3x = -0.23x-0.3
Since the equation of the line of symmetry is given, if we find the
equation of the parabola,
Check
y = a(x+3)¤ +q
If we substitute points (2, 6) and (-4, 3) into this equation,
6 = a¥25+q ……`①
17
3 = a¥1+q
……`②
If we solve for ① and ② simultaneously,
a=
7
, q=
Therefore, the equation of the parabola we are looking for is
y=
Numbers and Arithmetic
9
Students will learn sets, integers, and
rational numbers. Additionally,
calculation with square roots will be
introduced.
Variables and Equations
Students will learn how to identity,
solve, and apply equations. Systems of
equations and systems of inequalities
with variables will also be learned.
Basic Thinking Math
31
Level
Date
12
Name
The following are descriptions of the characteristics of deviation. Which is
false?
Relationships and Functions
Students will learn functions and
coordinates. Graphs of linear and
quadratic functions will also be
covered.
Performance
Assessment
① As the absolute value of deviation becomes smaller, the variable becomes
closer to the mean.
5cm
Find the volume of the prism whose base is
the trapezoid shown on the right and whose
height is 11cm.
② The degree of dispersal for the variables can be found by using the mean of
deviation.
Basic Thinking Math
31
Level
4cm
14
③ Deviation is the measure of the difference between the variable and the mean.
7cm
④ Deviation of variables less than the mean becomes a negative number.
The following figures are drawn to prove the Pythagorean Theorem.
Prove that a¤ +b¤ = c¤ .
⑤ The sum of deviations is 0.
The sum of the deviations is 0.
Therefore, the mean of deviations
is also 0.
A
Find the surface area of the cone shown on the right.
a
c
b
Proof
b-a
b-a
9cm
a
2
0
5
c
6cm
The data below show the deviations of Marcy’
s five math tests. Find the
standard deviation. (Round your answer to the nearest hundredth.)
-3
a
-4
Find the surface area and volume of each of the following solid figures.
The table below shows the deviations of five students’scores obtained
from target shooting practice. Find the following.
A
3cm
4cm
B
5cm
Student
A
B
C
D
E
Deviation
-4
x
4
2
8
10cm
B
Measure of x
B
b
a
c
a
a
c
c
Variance
c
b
9
・nopi MATH Level 26 Booklet 14
E・
Proof
10cm
b
A
b
a
Copyright ⓒ 1999, 2002-2004, 2007 by Daekyo Co., Ltd.
・nopi MATH is a registered trademark in Korea. Printed in Korea. www.enopi.com
E・
Revised by Drs. David L. Haury, Terri Teal Bucci & Hea-Jin Lee, at The Ohio State University
Probability and Statistics
12
Students will learn how to collect,
analyze, and graph simple statistical
data which can then be used to find
correlations. As well, the basic
properties of probability and statistics
will be introduced.
Measurement
Students will learn how to find angles,
lengths, areas, and volumes based on
concepts of geometric figures and
algebraic expressions. Finding
approximate values and properties of
trigonometric ratios will be also
introduced.
Geometry
Students will learn the concepts of basic
geometrical figures and use congruence
and similarity to prove their properties.
Other topics include the properties of
triangles and the Pythagorean Theorem
as well as the properties of circles.
5
입회상담자료집 2008.4.16 6:27 PM 페이지5
MAC52 2400DPI 175LPI T
Field of Study for E.nopi MATH
What is E.nopi’s Critical Thinking Math?
Levels 1-23
Critical Thinking Math
20
Level
20
The picture below follows an increasing pattern and the figure numbers
indicate the order. Answer the questions.
Critical Thinking Math
20
…
1
2
A Fill in each
3
21
The front, side, and top views of a set of blocks are given. Circle the correct set of blocks.
.
Front View
Number of dots( ) in
1
Number of dots( ) in
2
1`+`2` =
Number of dots( ) in
3
1`+`2`+`3` =
Number of dots( ) in
4
1`+`2`+`3`+`4` =
Figure number
Number of dots(
)
1
2
3
4
` 1
3
f
` aj
+2
+3
Top View
Side View
and complete the table.
B Using the pattern above, fill in each
C
Level
4
+
+
5
6
+
+
7
・・・
・・・
1
2
3
dots
How many dots( ) would there be in the 8th figure?
The number of
dots increases in the order of
1, 2, 3, .... Try finding the sums
of the consecutive numbers. Look,
1+2+3=4\3/2 and
1+2+3+4=5\4/2 !
12
13
Patterns and Relationships
(Algebra)
Students will use numbers, figures,
and arithmetic operations to learn
about sequences and develop an
understanding of basic equations.
Geometry
Students will develop an intuitive sense of
spatial relationships by using manipulatives.
Critical Thinking Math
10
Level
29
Circle the figure below that has the same area as the
.
Critical Thinking Math
21
Level
25
There are the following signs on Willy’s farm. But, the rain washed out some
parts of the signs. Find out the number of chickens and the number of
sheep. Answer the questions.
Number of cows: 10
Number of chickens: ?
Number of sheep: ?
Total number: 90
Total number of
legs of all the animals
240
①
②
③
④
Critical Thinking Math
22
Level
30
A How many chickens and sheep are there in total?
chickens and sheep
Harry, Jason, Jimmy, Hanson, and Kevin are in a race. Read the following
statements and answer the questions.
B Find the number of chickens and sheep. Fill in each
The total number of chickens and sheep is
•Harry is ahead of Jason, but behind Jimmy.
the legs of chickens and sheep is
•Hanson is ahead of Harry, but behind Jimmy.
.
If there are 80 chickens, the number of legs is
•Kevin is ahead of Hanson, but behind Jimmy.
.
, the sum of
and it is
less than 200.
If there are one less chicken and one more sheep, then the total
A From the first statement, list Harry, Jason, and Jimmy in order.
number of legs increases by
So, if
.
chickens are taken away from 80 chickens and
11
sheep are added, the total number of legs becomes 200.
B From the second statement, list Hanson, Harry, and Jimmy in order.
C How many chickens and sheep are there on Willy’s farm?
chickens
sheep
11
C From the third statement, list Jimmy, Hanson, and Kevin in order.
D From A and B, list Harry, Jason, Jimmy, and Hanson in order.
Problem Solving
E
From C and D, list Harry, Jason, Jimmy, Hanson, and Kevin in order.
11
Reasoning
(Reasoning and Proof)
6
Students will use classification and
analogy to develop analytical skills for
solving problems logically.
Students will learn 8 effective problem
solving strategies:
Problem solving by Pattern Recognition,
Data Analysis,
Alternative Methods,
Drawing Diagrams,
Deduction,
Trial and Error,
Reverse Calculation,
Problem solving Using Tree Diagrams.
Measurement
Students will compare the volumes of
different solids and become familiar
with measurement of length, area, and
volume.
입회상담자료집 2008.4.16 6:27 PM 페이지6
MAC52 2400DPI 175LPI T
Levels 24-32
Critical Thinking Math
24
Level
Date
19
Name
Find the sum of each set of 3 numbers in a horizontal, vertical, and diagonal
sequence in the following square.
Critical Thinking Math
6
1
8
7
5
3
2
9
4
25
Level
Date
1121 , 1211 , 1211
Horizontal
Vertical
19
Name
Diagonal
Dad sighs while reading the paper and says,“Gas prices are going up again.”
His son, Darren, thought about how he could help his father with this situation and
decided to look for ways to save money when buying gas for the car. He thought about
the different conditions and the different costs involved.
s look at Darren’
s calculations.
Let’
Squares and Magic Squares
The square is called a magic square when the numbers within the square have certain
inherent properties.
6 1 8
7 5 3
2 9 4
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
3_3 magic square
4_4 magic square
The sums of the numbers
in a horizontal, vertical,
and diagonal sequence
are all equal!
17
23
4
10
11
24
5
6
12
18
1
7
13
19
25
8
14
20
21
2
Darren’s family is going to an amusement park and they need to buy
gas at one of two nearby gas stations. Which of the two gas stations
would be better to use?
15
16
22
3
9
The table below shows the price of gas per liter at gas stations G and H.
5_5 magic square
It is called a 3_3, 4_4, or
5_5 magic square according
to the number of rows and
columns.
A
Consider this
•The horizontal line is called a row, and the vertical line is called a column.
•A magic square in which the number of rows and columns in n is called
an n_n magic square or a magic square of the nth degree.
▶ Note: An n_n magic square is read as an “n by n magic square.”
Example 3_3 magic square ⁄ three by three magic square
row
Gas Station
G
H
Price per Liter ($)
1.18
1.16
The table below shows the prices depending on the amount of gas purchased.
Complete the table.
Price per Liter($)
Amount of Gas
Purchased(L)
Station G
Station H
1
1.18_1 = 1.18
1.16_1 = 1.16
2
1.18_2 = 2.36
1.16_2 = 2.32
⋮
⋮
⋮
⋮
3
column
4
3
5
⋮
30
⋮
3
Problem Solving Ⅰ
(Numbers and Arithmetic)
Students will improve their problem solving ability and
be motivated by doing challenging mathematical puzzles
and quizzes.
Critical Thinking Math
28
Problem Solving Ⅱ
(Algebra)
Students will develop necessary problem solving skills
and realize how math can be useful and applicable
through solving problems based on real life situations.
Level
Date
21
Name
O
This is a game where a ball dropped at the
top bounces through a network of pins and
falls into a slot at the bottom, and whoever
correctly guesses the slot wins. As shown
on the right, the ball can be dropped at any
point, O, P, Q, R, or S, and each slot, A, B,
C, D, and E, has a different prize. Find the
expectation for each point.
A
P
R
S
$5 $0 $10 $0 $5
A B C D E
Critical Thinking Math
32
Level
22
If a ball is dropped at point O, write
the number of possible outcomes for
each space the ball can pass through.
(Use Pascal’s triangle.)
O
1
Look at the 7 solid figures made by placing cubes of 1cm adjacent to one
another in the box below and fill in the blanks.
1
1
1
2
$5
B
Q
1
$0
$10
$0
$5
In A, what is the expectation for the prize if you drop the ball at point O?
If you are not familiar with the
concept of expectation, read the
material on the next page and
come back to this problem.
•Solid figure with the smallest surface area and the fewest
number of vertices:
•Surface area:
cm¤
•Number of vertices:
Consider this
1
An arrangement of numbers with the pattern shown on
the right is called Pascal’s triangle.
1
1
1
1
2
3
4
1
3
6
…
1
1
4
1
15
The surface area is the area
of the faces on the surface.
When you count the vertices,
pay attention to where the
edges of the cubes meet.
Problem Solving Ⅲ
(Probability and Statistics)
Students will learn statistics to improve their problem
solving ability. This will also help them to understand
the value and usage of mathematics.
7
Spatial Sense
Students will improve intuitive insight and spatial
recognition with teaching tools such as Thinking
Bricks, Thinking Pentos, and Thinking Cubes.
7
입회상담자료집 2008.4.16 6:28 PM 페이지7
MAC52 2400DPI 175LPI T
Contents of E.nopi MATH
Basic Thinking Math is designed as follows.
Basic Thinking Math is composed of:
Review
Booklet Concept
Main Section
Try This 1, 2
Thinker’s Corner
Performance
Assessment/Comprehensive Assessment.
Basic Thinking Math
13
2
Basic Thinking Math
2
Review
Level
13
Level
Level
13
Date
Fill in the missing numbers.
Multiply. (6 points each)
1 2
4 5
8 9 10
6
1``1 12 13
15
16 17
19 20
Multiplication of 2-Digit
Numbers by 1-Digit
Numbers (10~8)
This booklet will continue to
have students practice
multiplying 2-digit numbers by
1-digit numbers with regrouping.
Name
2
Name
A
\ ``2 `3
\ 2 `2
:::::;;;;:
E
\ ``3 `5
\ 2 `6
::::;;:;;:
B
\ ``2 `3
\ 2 `3
:::::;;;;:
F
\ ``3 `5
\ 2 `7
::::;;:;;:
C
\ ``2 `3
\ 2 `4
:::::;;;;:
G
\ ``3 `5
\ 2 `8
::::;;:;;:
D
\ ``2 `3
\ 2 `5
:::::;;;;:
H
\ ``3 `5
\ 2 `9
::::;;:;;:
Date
4 `6
\ ` `7
;;;;;;;;;;;;;;;;;
4 `2
2 `8`
;;;;;;;;;;;;;;;;;
2 `2 `2
Basic Thinking Math
4 `6
\ ` `7
;;;;;;;;;;;;;;;;;
2
3
Booklet Concept
Review
Main Section
The cover page provides an overview
of booklet contents.
Each booklet begins with a review of
previously learned material.
Students learn mathematical skills and
techniques through drills in the Main
Section.
Basic Thinking Math
Try This
9
1
Level
The pirate is looking for his ship. Follow the correct difference to each
subtraction problem. (20 points)
Basic Thinking Math
Thinker’s Corner
5
2
Level
13
Let's play cards!
Pick a card and color the same numbered card below.
Divide. (5 points each)
• Lateral area = [
16
L
z5~/~3~=
z6~/~4~=
M
30~/~5~=
2z~/~7~=
N
63~/~9~=
32~/~4~=
42~/~7~=
m¤``
\~3.14~=
\~2~\~3.14]~\~
Surface area =
20-6
③ Place the cards face down
in a row.
12
18
z4~/~2~=
H
① Cut out the numbered cards.
20-3
17
8
• Base area = 6~\
G
m¤``
~ =
I
19
20-2
Assessment
. (50 points each)
A
② Shuffle the cards.
20-4
14
18
Comprehensive
Assessment
Fill in each
How to play
20-1
Performance
7
\~2~+
m¤``
=
④ Pick one card from the row
and turn it over.
40~/~8~=
O
K
36~/~6~=
P
B
20-9
1`0
20-5
J
15
20-7
16
1``1
17
18
19
20
Answer the question. (20 points)
20-7
• Base area =
1`4
13
Help students cut out the cards. Have students say the number on the card and
color in the correct card above.
Volume =
~\
cm¤``
\~3.14~=
\~
~
=
Q There are a total of 24 red, blue, and yellow sheets of paper. If there
are equal numbers of each color, then how many red sheets of paper
are there?
cm‹``
Number Sentence
Answer
8
16
17
18
19
20
・nopi MATH Level 23 Booklet 14
E・
15
Exceeds Standard
red sheets of paper
Meets Standard
Approaching Standard
Copyright ⓒ 1999, 2004, 2006 by Daekyo Co., Ltd.
・nopi MATH is a registered trademark in Korea. Printed in Korea. www.enopi.com
E・
Revised by Drs. David L. Haury, Terri Teal Bucci & Hea-Jin Lee, at The Ohio State University
・nopi MATH Level 14 Booklet 9
E・
Copyright ⓒ 1999, 2004, 2006 by Daekyo Co., Ltd.
16
・nopi MATH is a registered trademark in Korea. Printed in Korea. www.enopi.com
E・
Revised by Drs. David L. Haury, Terri Teal Bucci & Hea-Jin Lee, at The Ohio State University
8
Try This 1
Thinker’s Corner
Performance Assessment
This page fosters student interest
through the use of mazes, line
drawings, word scrambles, and codes.
Activities on this page challenge
students through the use of number
cards, number shapes, quizzes,
games, mazes, coloring activities,
folding papers, and stories.
This page reinforces the major concepts developed in
the booklet.
Comprehensive Assessment
The main concepts of each level are reviewed through
two Comprehensive Assessments at each level.
입회상담자료집 2008.4.16 6:29 PM 페이지8
MAC52 2400DPI 175LPI T
Critical Thinking Math is designed as follows.
Critical Thinking Math is composed of:
Booklet Concept
Review
Main Section
Concept Story/Concept Comic
Teaching Tools
Performance Assessment/Comprehensive Assessment.
Critical Thinking Math
1
Concept Story
Level
Critical Thinking Math
Performance
5
Concept Comic
Level
23
Critical Thinking Math
Comprehensive
Assessment
30
15
Level
Assessment
The picture below follows an increasing pattern and the figure numbers indicate the order. Answer
Wow, we’re under
the ocean !
the questions. (50 points each)
24
The picture below follows an increasing pattern and the figure numbers indicate
the order. How many dots( ) would there be in the 6th figure? (25 points)
dots
“Anna, let’s bake some
cookies in various shapes.”
...
Yay !!
1
“Yes, Mom! I’m going to make
triangular shaped cookies.”
3
2
Dogs...?
Well, class, what lives
in the ocean ?
4
・
・
・
1
2
A How many dots( ) would there be in the 5th figure?
An octopus !
3
4
dots
Whales !
B What figure number would have 18 dots( )?
Every exposed face of the blocks below was painted. How many faces were
Figure number
painted? (25 points)
Fish !
What ? Dogs ?
No, dogs live on land.
・nopi MATH Level 15 Booklet 20
E・
Copyright ⓒ 1999, 2004, 2006 by Daekyo Co., Ltd.
・nopi MATH is a registered trademark in Korea. Printed in Korea. www.enopi.com
E・
Revised by Drs. David L. Haury, Terri Teal Bucci & Hea-Jin Lee, at The Ohio State University
faces
7
7
15
Concept Story / Concept Comic
Performance Assessment
Stories and comics are used to cultivate student interest in mathematics.
Each comic has an underlying theme or concept that is being taught in a
humorous way. (Levels 1-4: Concept Story, Levels 5-23: Concept Comic)
This page reinforces the major concepts developed in the booklet.
Comprehensive Assessment
The main concepts of each level are reviewed through two
Comprehensive Assessments at each level.
Teaching Tools
Critical Thinking Math
5
Blocks and Shapes
Level
25
：3
Critical Thinking Math
Colored Blocks
9
Teaching Tools
Level
27
Use the given Colored Blocks shown to make the figure below. Trace the
outline of each block, and then write the block number in the correct space.
Use the given shapes from Blocks and Shapes to make the figure below, and
then trace the outline of each shape.
：3
Teaching Tools
Critical Thinking Math
Wooden Blocks
15
Level
27
Use 6 Wooden Blocks to make the figure below, and then trace the outline of
each block.
：1
15
15
15
Teaching Tools
Manipulatives are used to develop and enhance student ability with spatial relationships.
They also provide tangible experience with problem solving skills and concepts.
(Levels 1-6: Blocks and Shapes, Levels 6-14, 16-20: Colored Blocks, Levels 15-23: Wooden Blocks)
9
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MAC52 2400DPI 175LPI T
E.nopi MATH Teaching Tools
Students experience practical applications in mathematics by solving applied mathematical
problems using E.nopi MATH Teaching Tools.
Levels 1-23: Numerical Figures, Blocks and Shapes, Clear Paper, Colored Blocks, Mirror, and Wooden Blocks
Levels 24-32: Thinking Bricks, Thinking Pentos, and Thinking Cubes
Numerical Figures
Numerical Figures assist in developing the
concepts of number and quantity.
Colored Blocks
Colored Blocks assist in the
understanding of numbers as well as
length. As students manipulate Colored
Blocks, they develop their perception of
depth and location.
Thinking Bricks
10
Thinking Bricks consist of three cuboids
that can be used to stack up the bricks.
(5 pieces, 2 sets)
Blocks and Shapes
Blocks and Shapes assist in developing
depth perception by matching and finding
the location of various shapes.
Mirror
Mirror activities require students to
draw shapes symmetrically. This forms
the basis for line symmetry that will be
introduced in future studies.
Thinking Pentos
Thinking Pentos are used to build a
model built by putting the sides of unit
squares together. (12 pieces)
Clear Paper
Clear Paper is used to trace and copy
various shapes. This helps students to
develop their mental skills in relation to
depth perception and location.
Wooden Blocks
The manipulation of Wooden Blocks
enables students to learn depth perception,
location, and spatial relationships. This is
crucial in the development of critical and
analytical thinking skills.
Thinking Cubes
Thinking Cubes are used to build a model
that comprises the figures with concave
surface built by putting together the faces
of 3 or 4 cubes. (7 pieces)
입회상담자료집 2008.4.16 6:30 PM 페이지10
MAC52 2400DPI 175LPI T
E.nopi MATH is aligned with
school math curriculums
Numbers
(Levels 1-23)
Arithmetic
(Levels 1-23)
Number
and
Operations
Numbers and
Arithmetic
(Levels 24-32)
Patterns and
Relationships
(Levels 1-23)
Algebra
Geometry
(Levels 1-32)
Measurement
(Levels 1-32)
Variables and
Equations
(Levels 24-32)
Geometry
and
Measurement
Equations
(Levels 1-23)
Relationships
and Functions
(Levels 24-32)
Spatial Sense
(Levels 24-32)
Problem Solving
(Levels 1-23)
Grouping
(Levels 1-23)
Reasoning
and
Proof
Analogy
(Levels 1-23)
Probability and
Statistics
(Levels 24-32)
Problem
SolvingⅠ
Numbers and Arithmetic
Data Analysis /
Probability and
Problem Solving
(Levels 24-32)
Problem
SolvingⅡ
Algebra
Problem
SolvingⅢ
(Levels 24-32)
Probability and Statistics
(Levels 24-32)
Analysis
(Levels 1-23)
11
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MAC52 2400DPI 175LPI T
E.nopi MATH Study Program
Diagnostic
Assessment
Diagnostic Test
The diagnostic test measures the
weaknesses and strengths of the
student and evaluates the student’s
ability.
Initializing the
starting point of
E.nopi
Supplementing
the learning gaps
E.nopi covers all major
areas of mathematics.
Complementing students
academic progress with
additional studies
Mastery of all
successive E.nopi
curriculums
E.nopi improves
student performance
at school
E.nopi increases student
mathematical and analytical thinking
skills. This provides students with
greater opportunities for success in
and out of school.
Generating confidence,
instilling values
Greater self-confidence will have a
stronger impact on other areas of study.
12
E.nopi paves the
road to higher
learning
Starting Point
The starting point is where students
are most confident and comfortable.
This helps students to master the
current level ensuring future success
in succeeding levels.
입회상담자료집 2008.4.16 6:31 PM 페이지12
MAC52 2400DPI 175LPI T
E.nopi MATH Study Flow
Basic Thinking
YMC 02-13-2
Math
Performance
Asses
2
Level
13
Review
sment
Fill in each
g numbers.
Fill in the missin
. (50 points each)
A
4 5
1 2
9 10
8
6
15
13
12
1``1
20
19
17
16
Student
Reviews the previous booklet
and solves additional problems
in the review section.
• Base area =
• Lateral area
6~\
\~3.14~=
=[
m¤``
\~2~\~3.14]
~\~ ~ =
Surface area =
\~2~+
=
m¤``
m¤``
Instructor
B
• Base area =
~\
Volume =
E・
・nopi MATH
Level
\~3.14~=
\~ ~
=
Evaluates and assesses student
performance for the previous
booklet.
cm¤``
cm‹``
23 Booklet
14 Copyright ⓒ 1999,
E・
・nopi MATH
2004, 2006 by
is a registered
Daekyo Co., Ltd.
trademark in Korea.
Revised by Drs.
Printed in Korea.
David L. Haury,
www.enopi.com
Terri Teal Bucci
& Hea-Jin Lee,
at The Ohio State
University
2
Instructor checks for mistakes, evaluates the weaknesses for the
previous booklet, and previews the material for the new booklet.
Student & Instructor
Teaching Tools:
Numerical Figures
Guide
Critical Thinking
Math
24
2
Level
17
Level
13
Connection with
schoolwork
Connection with
•Variables and
Equations
2 Linear equation
s
•Relationships
and Functions
2 Rules and correspo
ndence
•Probability and
Statistics
2 Possible outcome
s
•Figures
2 Points, lines,
surfaces and angles
2 Polygons
2 Polyhedrons
•Geometry
2 Spatial figures
future learnin
g
•Probability and
Statistics
2 Possible outcome
s
2 Permutations
and combinations
2 Probability
Story
ers
Practicing Numb
Many people find
pleasure in solving
mathematical puzzles
lies in being able
to harmoniously
. The fascination
combine various
in math
divided into differen
fields of math
t branches such
that are general
as numbers, algebra
the magic of number
ly
, and geometry.
s by solving number
Let’s experience
puzzles.
up to 20 (6~5)
to teach
will continue
This booklet
1 to 20
numbers from
, match
students the
count objects
by having them in the blanks.
fill
numbers, and
Student & Instructor
Instructor introduces new materials
for the upcoming week and
instructs the student about the new
concept(s) that will be discussed.
Date
Name
Math
Basic Thinking
2
Study with Main Section, Try This, Thinker’s Corner, Concept Story / Concept Comic,
Teaching Tools, and other learning material.
Student
Basic Thinking
Basic Thinking
Math
24
Level
m and find each
Look at the diagra
2 3
1
natural numbers
4 5 6 7 8
Pick a card and
to 20
color the same
B
es of 4 are natural
How many multipl
or equal to 10?
numbers less than
es of 4 are natural
How many multipl
or equal to 20?
numbers less than
Find each of the
than or equal to
B
C
below.
numbered card
Wooden Blocks
Use 6 Wooden
each block.
Blocks to make
, and then
the shape below
25
e of
trace the outlin
20
② Shuffle the cards.
ed cards.
① Cut out the number
are
Notice that there
4 in
two multiples of
less
natural numbers
10.
than or equal to
less
For natural numbers
20, the
than or equal to
s of 4
number of multiple of
must be the quotient
20÷4.
③ Place the cards
in a row.
following.
es of 2 are natural
How many multipl
or equal to 15?
numbers less than
A
Teaching Tools
13
4
s of 4 and less
that are multiple
10÷4 = 2 R2
A
Math
16
Level
Level
How to play
17 18 19 20
13 14 15 16
9 10 11 12
s of
that are multiple
natural numbers
equal to 10
and less than or
natural numbers
of the following.
less than or equal
Critical Thinking
Math
2
rner
s!
Thinker’s Co
Let's play card
1
16
are natural
Since multiples
“less than 30”
numbers, we say
than or
is the same as“less
equal to 29.”
17
18
19
20
and
on the card
s say the number
Have student
cut out the cards.
Help students
card above.
color in the correct
es of 10 are natural
How many multipl
or equal to 100?
numbers less than
es of 6 are natural
How many multipl
30?
numbers less than
from the row
④ Pick one card
and turn it over.
face down
7
16
17
18
19
20
15
15
13
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MAC52 2400DPI 175LPI T
What are the benefits of E.nopi MATH?
14
1
Systematic study materials for all levels.
2
Study materials that develop the ability to solve problems independently.
3
An interactive teaching methodology that incorporates proactive feedback.
4
E.nopi helps students to develop their critical and analytical thinking skills.
5
E.nopi allows students to utilize their skills in all areas of study.
E.nopi MATH uses a systematic curriculum. The curriculum is divided into various levels according to
student abilities. This allows students to fully understand and master the required mathematical concepts
in a progressive manner. Questions in the curriculum are cumulative. Students will not be able to progress
if they do not understand or master the preceding concepts.
Some mathematical concepts are difficult to introduce. Some mathematical concepts are cumulative and
require extensive related knowledge of other mathematical concepts. The E.nopi curriculum is
progressive. Subtle increases in difficulty in each level makes it easy for all students to learn. This allows
students to become comfortable with all necessary concepts before proceeding to the next level. Students
will be able to solve questions that are presented as variations of similar concepts. Students will be able to
independently arrive at answers using their critical and analytical thinking skills.
E.nopi is a proactive learning process. Students receive continual, ongoing feedback from our
instructors to enhance the student learning process. Feedback from the instructors will include
review, performance assessment, and overview sheets. Instructors also work with parents to
maximize feedback. The parents receive and give feedback to both the instructors and their children.
Communication is an integral part of education. A positive environment makes learning optimal for
all students. In this case, students are able to learn from both their parents and instructors.
E.nopi MATH incorporates learning materials into its curriculum that will help students to develop
problem solving abilities. The active use of such materials creates a learning environment where students
will develop critical and analytical thinking skills. This is accomplished through developing depth
perception, and location and spatial relationship skills by utilizing our learning materials such as
Numerical Figures, Blocks and Shapes, Clear Paper, Colored Blocks, Mirror, and Wooden Blocks.
Difficulty and question variations are introduced systematically throughout all levels.
Performing well in E.nopi not only helps students in mathematics, but is also helpful for applying their
knowledge to other areas of academic studies. Skills that students will develop in E.nopi are broad. In
most cases, students will be ahead of their class and their peers. Ideally, students will advance faster in all
areas of academic studies and thus become more confident in mathematics and in other areas of study.
입회상담자료집 2008.4.16 6:31 PM 페이지14
MAC52 2400DPI 175LPI T
Three streams of learning
1
2
3
E.nopi Home Learning System
An E.nopi instructor visits the student’s home once a week for home instruction.
E.nopi In-Class Learning System
Students attend the closest E.nopi Learning Center twice a week for in-class instruction.
Correspondence System
Study materials are sent out to the student’s home via mail once a month.
※ Service availability can vary depending on the region.
Membership Fees
Initial Enrollment
$
Monthly Membership
In class instructor
Visiting instructor
$
$
Correspondence Course
$
※ Please contact your local office for registration.